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For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by -terms. We call the category -bicomplete if every -term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...
For an arbitrary category, we consider the least class of functors
containing the projections and closed under finite products, finite
coproducts, parameterized initial algebras and parameterized final
coalgebras, i.e. the class of functors that are definable by
μ-terms. We call the category μ-bicomplete if every μ-term
defines a functor. We provide concrete examples of such categories and
explicitly characterize this class of functors for the category of
sets and functions. This goal is achieved...
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